Creating and processing universal radar waveforms

ABSTRACT

A new approach to radar imaging is described herein, in which radar pulses are transmitted wi th an uneven sampling scheme and subsequently processed with novel algorithms to produce images of equivalent resolution and quality as standard images produced using standard synthetic aperture radar (SAR) waveforms and processing techniques. The radar data collected with these waveforms can be used to create many other useful products such as moving target indication (MTI) and high resolution terrain information (HRTI). The waveform and the correction algorithms described herein allow the algorithms of these other radar products to take advantage of the quality Doppler resolution.

BACKGROUND

1. Field

This disclosure relates generally to radar image processing, includingmethods and apparatus for creating and processing universal radarwaveforms.

2. Background

Radio detection and ranging (radar) technology transmit and receivepulsed electromagnetic waves to detect objects. In radar, anelectromagnetic pulse is transmitted from a radar platform, and thistransmitted pulse can be scattered back to the radar platform by variousobjects. The roundtrip time taken by the pulse to travel from the radarplatform to the scattering object and back therefrom may be proportionalto the distance between the radar platform and the object. Thetransmitted pulse may generally be sent with a characteristic waveformsuch that the returned pulse will be scattered back with a shaperesembling this transmitted waveform. Multiplying the returned energy bythis waveform may allow the returns to be sampled in time to yield asingle complex number representation for the returned energy as afunction of time—referred to as complex radar pulses. Since the complexradar pulses may be a function of time and the distance may beproportional to the roundtrip travel time of the pulses, these complexradar pulses can be thought of as samples of the objects present atvarious distances from the radar. This is how distance can be measuredusing a single radar pulse.

If two pulses are used, the line-of-sight motion of an object can alsobe determined. If the object is at a certain distance from the radarplatform and is moving toward the radar platform, then the complex radarpulses may rotate in phase with a positive frequency. Similarly, if theobject is moving away from the radar platform, then the complex radarpulses may rotate in phase with a negative frequency. This effect isreferred to as the Doppler effect. If multiple pulses at a givendistance are used in combination, multiple Doppler frequencies can bemeasured by decomposing the complex radar pulses into sine and cosinewaves at these frequencies. The energies observed at these variousfrequencies is called the Doppler spectrum.

However, if the radar platform is moving, then returns that appear atvarious Doppler frequencies can be the result of multiple stationaryobjects located at various different positions. For example, assume thata radar pulse is transmitted in a direction perpendicular to the motionof the radar itself and define the vector pointing from the radar to astationary object that scatters back pulse energy as the pointingvector. If the pointing vector to this object is perpendicular to thedirection of the radar motion, then the complex radar pulses for thisobject may appear at zero Doppler frequency. If, however, the pointingvector is positively aligned with the radar motion vector, then thecomplex radar pulses for this object may appear at a positive Dopplerfrequency proportional to the apparent line-of-sight motion of theobject relative to the radar platform.

This separation of stationary objects within a Doppler spectrum obtainedfrom a moving radar platform may have many different applications. Forexample, it is the foundation of what is called synthetic aperture radar(SAR) imaging. While the problems discussed herein are not limited toSAR imaging applications, SAR images provide an illustrative exampleuseful for describing deficiencies in the prior art. Those skilled inthe art will recognize that the problems addressed herein apply moreglobally to radar returns and the processing thereof, and are notlimited to their use in SAR images, which is only one example.

In SAR imaging, images are produced by post-processing a series ofcomplex radar pulses from a moving radar platform. In this imagingmethod, the Doppler resolution of a radar image (which relates to thedistance between objects perpendicular to the radar line-of-sight, ordistance in the cross-range direction) may be inversely proportional tothe length of the temporal aperture over which the Doppler decompositionis performed (this decomposition is also referred to as coherentintegration). Increasing the time over which coherent integration isperformed may provide finer cross-range resolution, which may be adesirable quantity for SAR imagery.

Multiple intelligence, surveillance and reconnaissance (ISR) missionsmay require different collection modes that may be mutuallyincompatible. For example, a common type of ISR mission for which SARradar platforms may be used is moving target indication (MTI) missions.MTI missions may require many pulses per detection opportunity alongwith a narrow beam. In contrast, detailed imaging missions may requirethe collection of continuous pulse streams using broad beams. As thesemodes may be inherently incompatible, no MTI information may beavailable during image mode collection and vice versa.

One approach that may be taken to address the incompatible modes ofoperation under which the radar platform is required to collect data isto have the radar platform transmit pulses for both modes over the sametime period. However, assuming that a fixed number of samples may betransmitted and collected over the same time period, the radar resourcescollected over the same time period for each mode may be effectivelyhalved. This can result in a dramatic, corresponding decrease in thequality of resulting SAR images.

In short, generating high quality SAR images using existing radarimaging schemes may require numerous radar resources. For example,existing radar imaging schemes may be directed to using samplingpatterns that allow for straightforward processing to generate the radardata output. While existing sampling patterns may have known andstraightforward processing techniques, they may require a high number ofpulses and a large amount of radar resources. Any reduction in thenumber of pulses may result in significant degradation in processedradar returns.

U.S. patent application Ser. No. 12/026,508, entitled “Method andApparatus for Creating and Processing Universal Radar Waveforms,” filedFeb. 5, 2008, attorney docket number 81085-12, discloses a time domainapproach that addresses these problems, the entire content of which isincorporated herein by reference. However, applicants have sincediscovered other approaches which provide even greater flexibility.

SUMMARY

A radar transmission system may include a transmitter system and anantenna system.

The transmitter system may be configured to generate one or more radarsignals.

The antenna system may have spatially-separated elements and may beconfigured to radiate the one or more radar signals from thespatially-separated elements.

The transmitter system and/or the antenna system may be configured suchthat the radiated radar signals include a pattern of spatially-separatedradar pulses, each from a different one of the spatially-separatedantenna elements. The pattern of pulses may have at least twoneighboring radar pulses that have a spatial separation that issubstantially unequal to the spatial separation between at least twoother neighboring radar pulses in the pattern of pulses, a mainloberadiation pattern with a width that is near or substantially equal tothe minimum possible mainlobe width, and/or sidelobe radiation patternswith substantially even energy distribution.

The radar transmission system may include a processing system configuredto generate pulses using a Fourier transform which are used by thetransmitter system to generate the one or more radar signals.

The radiated pattern of pulses may have a quadratic residue (QR) patternor a pseudo-random pattern.

The elements of the antenna system may be spatially-separated in twodimensions. The pattern of radar pulses may include pulsesspatially-separated in the two dimensions. The substantially unequalseparation may include substantially unequal separation in the spatiallocations from which the radar pulses are radiated by the antenna systemin both of the two dimensions.

The transmitter system may be configured such that the radiated radarsignals include a pattern of time-separated radar pulses having at leasttwo sequential radar pulses with a time separation that is substantiallyunequal to the time separation between at least two other sequentialradar pulses in the pattern of pulses.

The antenna elements may be unequally spaced.

The antenna elements may be equally spaced, but the transmission systemmay be configured to selectively drive the elements so as to cause thedriven elements to have the substantially unequal spatial separations.

A radar reception system may include a receiver and a processing system.

The receiver may be configured to receive a radar signal which includesa first data set having a plurality of values based on a radar waveformreturn from a set of transmitted radar pulses.

The processing system may be configured to create a second data setcomprising the first data set minus at least one significant value fromthe first data set and its effects on other values within the first dataset. This may occur when the set of transmitted radar pulses wastransmitted with a spatial separation between at least two neighboringpulses that is substantially unequal to the spatial separation betweenat least two other neighboring pulses in the set, a mainlobe radiationpattern with a width that is near or substantially equal to the minimumpossible width, and/or sidelobe radiation patterns with a substantiallyeven distribution of energy.

The processing system may be configured to create a third data setcomprising the at least one significant value from the first data set,and to combine the second and third datasets.

The first data set may include a plurality of transformed values. Theradar plurality of transformed values may be frequency values.

The at least one significant value may include a peak value in afrequency domain.

The second data set may include a number of peak values from the firstdata set chosen based on predetermined selection criteria.

The processing system may be configured to determine the effects of theat least one significant value by calculating a plurality of propagatedeffects from the at least one significant value.

The processing system may be configured to create the second data set byidentifying at least one peak value in the first data set, creating apeak correction function approximation using the at least one peakvalue, and removing the peak correction function approximation from thefirst data.

The pattern of radar pulses may include pulses spatially-separated intwo dimensions, and the substantially unequal separation includessubstantially unequal separation in both of the two dimensions.

The radiated radar signals may include a pattern of time-separated radarpulses having at least two sequential radar pulses with a timeseparation that is substantially unequal to the time separation betweenat least two other sequential radar pulses in the pattern of pulses.

The pattern of radar pulses may have at least two neighboring radarpulses that have a spatial separation that is at least twice theshortest spatial separation between at least two other neighboring radarpulses in the pattern of pulses.

Non-transitory, tangible, computer-readable storage media may containprogramming code which, when executed by a computer system, causes theradar transmission and/or reception systems to function as recitedherein in whole or in part.

These, as well as other components, steps, features, objects, benefits,and advantages, will now become clear from a review of the followingdetailed description of illustrative embodiments, the accompanyingdrawings, and the claims.

BRIEF DESCRIPTION OF DRAWINGS

The drawings disclose illustrative embodiments. They do not set forthall embodiments. Other embodiments may be used in addition or instead.Details which may be apparent or unnecessary may be omitted to savespace or for more effective illustration. Conversely, some embodimentsmay be practiced without all of the details which are disclosed. Whenthe same numeral appears in different drawings, it refers to the same orlike components or steps.

FIG. 1 compares plots of various universal radar waveform (URW) samplingpatterns of length 41, including a full pattern, a first-half pattern,an alternating pattern, a quadratic residue (QR) pattern and apseudo-random pattern.

FIGS. 2A-E compare plots of the frequency response for the URW samplingpatterns shown in FIG. 1.

FIG. 3 is a table of binary patterns of a first dozen linear quadraticresidue (QR) patterns.

FIG. 4 compares plots of QR patterns, each of a particular samplingpattern length (p), including p=41, p=83, p=197, p=199 and p=257.

FIGS. 5A-E compare plots of frequency responses for the various lengthsof QR patterns of FIG. 4.

FIGS. 6A-E compare plots of interpolated frequency responses for thevarious lengths of QR patterns of FIG. 4.

FIGS. 7A-E compare plots of interpolated frequency responses for variousURW sampling patterns of length 257, including a full pattern, afirst-half pattern, an alternating pattern, a QR pattern, and apseudo-random pattern.

FIGS. 8A-E compares zoomed plots (showing the details of the main lobe)of frequency responses for the various sampling patterns of FIG. 7.

FIG. 9 is a plot of a Rule 30 update function for a cellularautomaton-based pseudo-random number generator.

FIG. 10 illustrates a 50 step update of the Rule 30 cellular automatonof FIG. 9.

FIGS. 11A-D compare synthetic aperture radar (SAR) images obtained usingvarious subaperture sampling patterns of length 41, including fullpattern, first-half pattern alternating pattern, and quadratic residuepattern.

FIGS. 12A-B show a plot of a maximum sidelobe level of a QR pattern as afunction of pattern length as compared to a plot of a mean sidelobelevel.

FIGS. 13A-C compare plots of true spectrum of a test data, approximationto the true spectrum, and corresponding error of the approximation tothe true spectrum.

FIG. 14 is a flow diagram illustrating a peak correction process.

FIGS. 15A-C are a compilation of plots illustrating the operation of thepeak correction process of FIG. 14.

FIGS. 16A-C are plots of an approximation to the true spectrum as shownin FIGS. 13A-C when sampled using QR pattern with the peak correctionprocess of FIG. 14.

FIG. 17 is a block diagram illustrating a pair of transformations usedto provide input data to an iterative process of the peak correctionprocess of FIG. 14.

FIG. 18 is a block diagram detailing the iterative process of the peakcorrection process of FIG. 14.

FIG. 19 is a block diagram illustrating the final step of the peakcorrection process.

FIGS. 20A-B compare a SAR image captured using a full set of pulses to asecond SAR image obtained using a QR pattern with peak correction.

FIG. 21 illustrates the two dimensional URW code where the onedimensional URW codes are quadratic residue (QR) codes of length 41 and43, respectively.

FIG. 22 shows the URW response function for the two-dimensional URW codeillustrated in FIG. 21 in logarithmic units.

FIG. 23 is a block diagram of a radar system that may be used in thegeneration, transmission, and receipt of the URW.

DETAILED DESCRIPTION

Illustrative embodiments are now discussed. Other embodiments may beused in addition or instead. Details which may be apparent orunnecessary may be omitted to save space or for a more effectivepresentation. Conversely, some embodiments may be practiced without allof the details which are disclosed.

The word “exemplary” is used herein to mean “serving as an example,instance, or illustration.” Any embodiment described herein as“exemplary” is not necessarily to be construed as preferred oradvantageous over other embodiments. In addition, the headings andsub-headings used herein are not to be taken as limiting in any senseand are used for ease of reference to the various parts of the document.

The techniques described herein may use fewer radar resources whilemaintaining the quality of processed radar returns. SAR images will beused in a demonstrative fashion to help illustrate the technologiesdisclosed herein. However, the technologies are not limited to use withSAR images, and those skilled in the art will recognize theirapplicability to a wide range of radar applications. For example, thetechnologies described herein are applicable to applications such asmoving target indication (MTI) and high resolution terrain information(HRTI).

With standard, evenly sampled SAR waveforms, image resolution may becomefiner as the temporal aperture (i.e., the period of time during whichthe radar pulses are transmitted) used for coherent integrationincreases. In one approach, an uneven sampling waveform, coupled withappropriately tailored post-processing algorithms, is used to produceimages of similar quality and fewer radar pulses over the same temporalaperture.

The pulse repetition frequency (PRF) of a radar waveform is equal to thenumber of pulses that are transmitted by the radar per second. Theinverse of this baseline PRF is a time increment (Δt) that is thesmallest time increment between pulses. A universal radar waveform (URW)is defined as a function of a radar waveform that transmits pulses at abaseline PRF. In one exemplary approach, the URW is constructed of aradar waveform that includes pulses transmitted at multiple PRFs, witheach PRF being a multiple of the baseline PRF.

In one exemplary approach, the URW is defined in increments of Δt (i.e.,the inverse of the baseline PRF) such that the time separation betweenpulses is equal to integer multiples of Δt. For example, if a baselinePRF is 10 pulses/second, then a standard waveform over the course of 1second would consist of 10 pulses, each separated in time by 0.1seconds. Thus, in this approach, the URW may be defined by pulses thatare separated by times that are multiples of 0.1 seconds (0.2, 0.4, 0.5,etc.). For example, a series of pulses that are transmitted over 1second may be described as follows: Pulse 2 is transmitted 0.2 secondsafter Pulse 1, Pulse 3 is transmitted 0.1 seconds after Pulse 2, Pulse 4is transmitted 0.4 seconds after Pulse 3, and Pulse 5 is transmitted 0.2seconds after Pulse 4.

A convenient representation of the URW is one where a binary string ofones and zeros represents when pulses have or have not been transmitted.For example, utilizing the 1 second example again, if a one (“1”)represents that a pulse is transmitted at that integer multiple of Δtand a zero (“0”) represents that a pulse is not transmitted at thistime, the previous URW example can be represented by a 10 characterbinary string [1,0,1,1,0,0,0,1,0,1]. Similarly, a standard waveformtransmitting 10 pulses, each separated by 0.1 seconds, can berepresented as [1,1,1,1,1,1,1,1,1,1].

The definition for the URW is flexible and general in its application.For example, if the desired shortened separation between pulses is notan integer multiple of a predefined Δt, then the baseline PRF can besufficiently increased (and thereby the Δt can be decreased) such thatall time separations between pulses can be defined in terms of integermultiples of this new Δt. Conversely, the baseline PRF can besufficiently decreased if a larger separation between pulses is desired.In this manner, the URW is a general representation of an unevenlypulsed waveform that can be defined in terms of a sparse, unevensampling of a waveform with a baseline PRF.

This binary string representation can be thought of as a samplingpattern of the underlying baseline PRF. For example, the exemplary URWabove (i.e., [1,0,1,1,0,0,0,1,0,1]) can be described as a samplingpattern of the same binary sequence multiplied by the baseline PRFrepresentation, since[1,0,1,1,0,0,0,1,0,1]×[1,1,1,1,1,1,1,1,1,1]=[1,0,1,1,0,0,0,1,0,1].Examples of various URW sampling patterns are shown in FIG. 1, whichcontain plots of the URW sampling patterns of length 41, respectivelyreferred to as a full pattern (plot 102), a first-half pattern (plot104), an alternating pattern (plot 106), a QR pattern (plot 108), and apseudo-random pattern (plot 110).

In radar imaging, the frequency response of the URW pattern can be veryimportant. The URW representation described above allows the analysis ofboth the frequency response of the sampling pattern and how the samplingpattern affects the characteristics of the waveform itself. Since theURW is defined as a function of time (e.g., integer increments of Δt), aFourier representation (decomposition in sine and cosine waves) showshow the URW is defined in frequency. Different radar applications may beoptimized by ensuring or designing certain characteristics in theFourier transform of the URW. With the inventive sampling and processingtechniques disclosed herein, these characteristics may be selected andutilized without sacrificing operational efficiency or radar outputqualities.

For SAR images, for example, the narrowness of the width of the mainlobe of the URW frequency response corresponds to the radar imagingresolution, and the integrated sidelobe energy corresponds to blurringof the radar image. Therefore, the best qualitative sampling pattern forSAR applications may have a frequency response with both a narrow mainlobe and small sidelobes, though some tradeoffs between the two areinevitable. A narrow main lobe may mean that the bulk of the energyresponse occurs in a narrow frequency range; this may indicate that theobserved energy at a particular frequency generally occurs as the resultof energy that is actually present at that frequency and no others. Flatsidelobes may mean that frequencies other than that of the main lobehave low energy responses; this may indicate that the observed energy ata particular frequency generally does not respond to frequencies otherthan the frequency of interest. In other words, having flat sidelobesmay mean that the resultant sidelobe energy of the waveform frequencyresponse is distributed as evenly as possible. This even distributionmay ensure that any single sidelobe peak is as low as possible relativeto the main lobe peak. Flat sidelobes may maximize the mainlobe-to-maximum sidelobe energy ratio. Those skilled in the art willrecognize and appreciate that other radar applications may havedifferent desired optimal Fourier transform characteristics. Generallyspeaking, the sampling and processing techniques disclosed herein mayallow for such characteristics to be chosen and applied for any givenapplication, not limited to SAR imaging.

To provide further background to the use of URW, some details ofsampling data using even and uneven sampling will be discussed.

Two regular patterns (those whose sampling is more even or regular)using about half of the pulses of a full sampling pattern will becompared to the full sampling pattern: the first-half pattern and thealternating pattern. These patterns are shown visually in the firstthree plots of FIG. 1, and the frequency response of each can be seen inFIGS. 2A-E, which illustrates the frequency response interpolated by afactor of eight for the following URW sampling pattern of length 41shown in FIG. 1: the full pattern 102 (plot 202, FIG. 2A), thefirst-half pattern 104 (plot 204, FIG. 2B), the alternating pattern 106(plot 206, FIG. 2C), the QR pattern 108 (plot 208, FIG. 2D), and thepseudo-random pattern 110 (plot 210, FIG. 2E).

The main lobe width is twice as wide for the first-half pattern than forthe full pattern, effectively making the SAR image resolution coarser bya factor of two. In addition, the sidelobes are wider by the same factorand pushed out in frequency by a factor of two, though they decay inmuch the same way as the full pattern. Similarly, just as a ½ samplingmakes the image resolution more coarse by a factor of 2, a 1/n samplingpattern makes the image resolution more coarse by a factor of n.

The alternating pattern has a different frequency response. The mainlobe width is the same as the fully filled case, and the first fewsidelobes decay just as quickly. However, a significant differenceoccurs near frequencies that are one-half the PRF (also referred to asthe Nyquist frequency), where a large sidelobe response is seen at thesefrequencies from the alternating pattern. Using every n-th sample notonly has the same narrow main peak and large near Nyquist sidelobes, butother large sidelobes as well. Accordingly, reducing the sampling by 50%or more but retaining an even sampling pattern has the undesired effectof reducing the quality of radar output data (including but not limitedto output data useful for generating SAR images).

The first of two types of uneven sampling patterns will now bedescribed. As mentioned previously, one goal may be to generate anequivalent quality SAR image using fewer radar pulses than standardmethods. As shown above, some patterns using fewer pulses have frequencyresponses with a narrow main lobe, yet their sidelobes are high. Othershave flatter sidelobes, yet their main lobe widths are wider. For theURW, a sampling pattern is sought that can provide a narrow main lobeand flat sidelobes in the same pattern.

In one approach, one set of sampling patterns that have these desiredURW properties may be those that implement a property of number theoryreferred to as the quadratic residue. For background, modular arithmeticuses only the numerical remainder that results when one integer isdivided by another integer. For example, 15 mod 4 is notation thatrefers to the remainder that results from dividing the integer 15 by theinteger 4. The integer 4 divides into 15 three times, which leaves aremainder of 3. Therefore 15 mod 4 is 3. A quadratic residue is thendefined as follows. Let p be an odd prime number (or any prime numbergreater than 2). Further, an integer i is said to be a quadratic residueof p if and only if there exists an integer r, where 0<r<p and that r²=imod p.

For example, let 5 be the prime number of interest, p. Therefore, forr=[1,2,3,4], the squares of r (r²=[1,4,9,16]) are divided by p and theirrespective remainders ([1 mod 5, 4 mod 5, 9 mod 5, 16 mod 5]=[1,4,4,1])are found. Therefore, from this definition, the integers 1 and 4 areconsidered to be quadratic residues.

Additionally, quadratic residue patterns have interesting propertiesbased upon the value of the prime number p. For odd prime numbers, thesenumbers can either be 1 mod 4 (where p mod 4=1 mod 4=1) or 3 mod 4(where p mod 4=3 mod 4=3). With these definitions, a URW samplingpattern can be established, with the URW sampling pattern based onquadratic residues being called herein quadratic residue pattern (or QRpattern) and is defined as follows. Let w(i) be the URW sampling patternof length p (for which w has index values ranging from 0 to p−1). If p≡1mod 4, then w(0)=0, w(i)=1 if i is a quadratic residue of p, and w(i)=0otherwise. If p≡3 mod 4, then w(0)=1, w(i)=1 if i is a quadratic residueof p, and w(i)=0 otherwise. FIG. 3 illustrates the binary patterns of afirst dozen linear QR patterns.

As a property of quadratic residues from number theory, it can be shownthat for any odd prime p, there are exactly (p−1)/2 integers that arequadratic residues of p, and therefore exactly (p−1)/2 integers that arenot quadratic residues of p (zero is not defined to be either aquadratic residue or not a quadratic residue). Depending on the value ofthe pattern when i=0, this essentially partitions the sample space intotwo equal pieces. FIG. 4 compares plots of QR patterns for variouslengths, including p=41 (plot 402), p=83 (plot 404), p=197 (plot 406),p=199 (plot 408) and p=257 (plot 410), and the plots of their respectivediscrete frequency responses are shown in FIGS. 5A-E, including p=41(plot 502, FIG. 5A), p=83 (plot 504, FIG. 5B), p=197 (plot 506, FIG.5C), p=199 (plot 508, FIG. 5D) and p=257 (plot 510, FIG. 5E).

One property of QR patterns that is beneficial for the URW is that QRpatterns may have nearly or identically equal sidelobes at discretefrequencies. Depending on the value of p mod 4, the sidelobes may beeither nearly flat (p≡1 mod 4) or perfectly flat (p≡3 mod 4), as can beseen in FIGS. 5A-E. Though QR patterns of length p≡3 mod 4 may be flatwhen sampled discretely, the plots of the oversampled frequencyresponses contained in FIGS. 6A-E, which contain plots of interpolatedfrequency responses for QR patterns of various lengths, including p=41(plot 602, FIG. 6A), p=83 (plot 604, FIG. 6B), p=197 (plot 606, FIG.6C), p=199 (plot 608, FIG. 6D) and p=257 (plot 610, FIG. 6E), illustratethat QR patterns of length p≡1 mod 4 also have relatively flatsidelobes.

Looking again at the frequency plots, the QR pattern seems to be theperfect balance between sidelobe level and main peak width. In fact, thedescription of the QR pattern above demonstrates that the main peakwidth may be the same width as the full pattern, while the sidelobes arerelatively flat.

FIGS. 7A-E contain plots of the interpolated frequency responses for thefollowing sampling schemes of length 257: full pattern (plot 702, FIG.7A), first-half pattern (plot 704, FIG. 7B), alternating pattern (plot706, FIG. 7C), quadratic residue pattern (plot 708, FIG. 7D), andpseudo-random pattern (plot 710, FIG. 7E). FIGS. 7A-E show the fullfrequency range, while FIGS. 8A-E contain close-up plots of the mainpeak and the first few sidelobes of the frequency response for the samesampling patterns of length 257: full pattern (plot 802, FIG. 8A),first-half pattern (plot 804, FIG. 8B), alternating pattern (plot 806,FIG. 8C), quadratic residue pattern (plot 808, FIG. 8D), andpseudo-random pattern (plot 810, FIG. 8E). The frequency response plotsof the length 257 patterns in FIGS. 7A-E can be compared to the length41 patterns in FIGS. 2A-E.

Another consideration for uneven sampling may come from the idea ofrandom or pseudo-random patterns covering the desired fraction of radarpulses. The frequency response of such patterns may have a narrow mainpeak width and low sidelobe levels. While these properties may not beachieved by all random patterns nor quite as well as the QR patterns,the flexibility of designing uneven sampling patterns of arbitrarylength and fraction of pulses may make such patterns useful.

One approach for implementing a pseudo-random generator is a cellularautomaton-based generator. A cellular automaton may be a rules-basedcomputational network comprised of connected elements in the form of anarray, where each cell may compute an output state as a function of itsinputs and a computational rule set. In a one-dimensional cellularautomaton of radius 1, a cell in the network may compute its outputstate based upon inputs of itself and the two nearest cells along asingle one-dimensional line. All cells in the array may be updatedsimultaneously, and the updated value of the cell at the next time stepmay be a function of the inputs from the previous time step. FIG. 9illustrates a plot 900 of a Rule 30 update function, where a white cellrepresents that the cell value is equal to “0” and a black cellrepresents that the cell value is equal to “1.” The output state of thecell is provided at the bottom as a function of the configuration ofinput cells.

For example, reviewing the first section 902 of the plot 900, if thecell has a value of “1” and each of its neighbors also has a value of“1,” then the updated value of the cell would be “0.” Since there arethree inputs, each having possible values of “0” and “1,” there are 2^3or 8 possible input configurations. The update function or “rule”defines the output states that occur in the presence of each possibleinput configuration. The rule numbering system is defined as the base 10number represented by the binary output string above −00011110=30.

Time evolution of the Rule 30 cellular automata network may yield randomproperties which can be used to generate pseudo-random numbers havingbeneficial URW properties. FIG. 10 illustrates a 50 cell array 1000 witha time evolution of 25 updates using Rule 30 cellular automaton. Therandom number sequence used for URW sampling is taken from the centercolumn of this evolution. The frequency plots of the Rule 30 patterns oflength 257 are shown in FIGS. 8A-E and 7A-E.

The goal of achieving high quality radar output data (e.g., for highresolution SAR images) using fewer radar pulses may require a number ofsignal processing advancements. Consider first the case of halving thenumber of radar pulses (which would allow for simultaneous imaging oftwo disparate areas, for example). FIGS. 11A-D illustrate SAR imagesobtained using 32 pulses per subaperture, with subaperture samplingpatterns of length 41 including a full pattern (image 1102, FIG. 11A), afirst-half pattern (image 1104, FIG. 11B), an alternating pattern (image1106, FIG. 11C) and a QR pattern (image 1108, FIG. 11D). The final threeimages (1104, 1106, 1108, FIGS. 11B-D) are generated using approximatelyone-half of the pulses used for first image (1102, FIG. 11A).

A number of non-ideal solutions to the problem will be described hereinand shown with phase history data in FIGS. 11A-D to describe themotivation behind URW and illustrate certain improvements achieved bythe techniques disclosed herein. The test data being used comes from animage that has two corner reflectors (at the left edge and the upperright portion of the image) in addition to a few other brightreflectors, as well as some low cross-section road-like or runway-likefeatures.

One approach to generate SAR imagery with half the number of radarpulses may be to reduce the dwelling of the radar platform over thetarget by a factor of two. Because, in this case, the image resolutionmay be proportional to the temporal aperture used for coherentintegration, the image may have a coarser resolution (by the same factorof two). In addition, the sidelobe peaks may be visible in that imageand the low cross-section targets may be slightly less well resolved.

One alternative may be to use alternating pulses—spread the pulses outevenly over the same temporal aperture. Unfortunately, this pattern mayhave a frequency response that has a large secondary peak near Nyquistfrequency. This may indicate that strong scatterers from frequenciesnear the Nyquist frequency will also be seen at zero frequency, whichmay create ghost images of the same corner reflector in the respectiveSAR image. The large sidelobes of the alternating pattern frequencyresponse also almost completely blur the low cross-section features.

Unfortunately, as illustrated in FIGS. 11A-D, the image quality achievedusing a QR pattern of length 41 may be poor because the low differencein levels of the sidelobes relative to the main lobe (also referred toas the dynamic range of the sampling pattern) blurs both the high andlow cross-section targets in the image. Using any of these samplingpatterns inside each of subapertures (instead of uneven sampling on thesubaperture level) may have deleterious effects on image quality aspredicted by the frequency responses of those patterns.

There may be little that can be done to improve the inherent sidelobelevels of a 50% sampling pattern, other than make the sidelobe patternrelatively flat and the main peak width as narrow as possible—the QRsampling pattern tends to achieve this best. Increasing the length ofthe QR pattern may improve the sidelobes gradually, as seen in FIGS.12A-B, illustrating a plot 1202 (FIG. 12A) of the maximum sidelobe levelof the QR pattern as a function of pattern length as well as a plot 1204(FIG. 12B) of mean sidelobe level as a function of pattern length.Changing the sampling or adding complex weights to the pattern may notsignificantly improve the pattern's effects on the generated SARimagery. However, in accordance with one approach, a correctionalgorithm can be applied to correct for the sampling pattern effects.This is described further herein.

To correct for the effects of a URW sampling pattern, known propertiesof the sampling pattern and their propagated effects may be leveraged inthe decoding process. For example, the QR pattern (and the pseudo-randompattern) may have a narrow main lobe, which implies that what isobserved in the Doppler spectrum at a particular frequency may bepredominately the result of energy at that frequency and little energyfor other frequencies. This may provide a level of confidence thatstrong scatterers in a SAR image constructed with a QR pattern will bewell resolved and will not be significantly corrupted from energyelsewhere in the image.

Using this fact, a reasonable confidence level may be reached as to howthe energy of this complex scatterer will propagate through the SARimaging process via the sampling pattern response. Those skilled in theart will recognize propagation patterns and effects of other samplingpatterns. In any event, iterative correction for complex scatterers maybe used to remove the blurring effects observed in previous figures andresulting in a SAR image with better quality. To illustrate themotivation behind this process, first consider an example ofapproximating a spectrum consisting of ten discrete delta functions,whose periodogram is shown in FIGS. 13A-C, illustrating a true spectrumof test data (plot 1302, FIG. 13A), an approximation to the truespectrum when sampled using length 1021 QR pattern (plot 1304, FIG.13B), and the corresponding error (plot 1306, FIG. 13C). When arepresentative time series is sampled unevenly, like the QR whosefrequency response is shown in plot 1304 (FIG. 13B), the resultingperiodogram straightforwardly constructed from half of the timemeasurements may be far inferior. Without additional processing, much ofthe true spectral energy may be spread into other frequencies.

Still, each of the ten peaks can be discerned in the length 1021 QRspectral approximation, because they are visible within the dynamicrange limitations of the sampling pattern. Taking into account thesampling effects, iterating over individual peaks or groups of peaksthat are detected above a predetermined threshold related to thesampling pattern dynamic range, a much better approximation to thespectrum may be obtained.

FIG. 14 illustrates an overview of a peak correction process 1400 thatsets a threshold as appropriate to the uneven sampling pattern, and theniteratively processes the peaks in the sampling pattern. The descriptionof the peak correction process 1400 will also refer to FIGS. 15A-C,which contains a plot of a measured spectrum 1502 (FIG. 15A). In step1402, a peak over the threshold in the current unevenly sampled spectrumapproximation is detected. In one approach, this is the complexamplitude of the largest peak, as shown in 1504 (FIG. 15B). In step1404, the complex peak amplitude of the detected peak is added to thepeak correction spectrum approximation. In step 1406, any samplingpattern effects due to the detected peak are removed from the currentunevenly sampled spectrum approximation. In one approach, a QR samplingresponse of the point source 1504 (FIG. 15B) is calculated andsubtracted from the measured spectrum 1502 (FIG. 15A), generating aresulting spectrum 1506 (FIG. 15C) with the QR sampling responsesubtracted. Then, as determined in step 1408, the process stops when thecurrent unevenly sampled spectrum approximation is near the noise levelof the detector. This peak correction process 1400 may be stable, so anover-aggressive stopping condition may have little effect on thespectral approximation.

FIGS. 16A-C contain a plot of an approximation of a test spectrum (plot1602, FIG. 16A) when sampled using a QR pattern after the peakcorrection process 1400 has been applied (plot 1604, FIG. 16B). FIG. 16Calso contains a plot of the corresponding error (plot 1606). Asillustrated in plot 1604 (FIG. 16B), this approximation detects all tenof the actual peaks in the data. The difference between plot 1604 (FIG.16B) and plot 1304 of FIG. 13B, which is a plot of the approximation tothe true spectrum when sampled using length 1021 QR pattern, is visuallyapparent. A characteristic of the peak correction process 1400 may bethat it generally performs better with strong peaks, therefore itsapplication to SAR imaging may improve most near strong features thatare likely to be of interest.

FIG. 17 illustrates the setup for the peak correction process 1400, withan FFT block 1704 converting a waveform sampling w(t) in the time domain1702 into a waveform response function W(f) in the frequency domain1706, and an FFT block 1714 converting a set of received complextemporal data (a first dataset) z(t) in the time domain 1712 to a set ofcomplex frequency data (a transformed version of the first dataset) Z(f)in the frequency domain 1716. The process then proceeds with FIG. 18,where a second dataset 1802, which is initially equal to the transformedversion of the first dataset Z(f) 1716, is processed by step 1804 suchthat at least one significant value from the second data set isselected. The second data set 1802 will also be referred to as aresidual dataset. Then, operation continues with step 1806, where the atleast one selected significant value is convolved with the waveformresponse function W(f) 1706, the result of which is subtracted from thesecond data set in step 1808. Further, a third dataset 1812 is createdfrom step 1810, where the at least one selected value in step 1804 isadded to previously selected significant values. Thus, the third dataset1812 contains a sum of selected values.

FIG. 19 is a block diagram detailing an optional final step of the peakcorrection process 1400, where a final version of the second data set1902 is added to a final version of the third dataset 1904 in block 1906to create a combined dataset 1908. In various approaches, the term“combine” is used to describe generally what may be done with theresidual dataset of second dataset 1802. For example, the residualdataset may be added back in with a multiplicative weight of one, whilea multiplicative weight of zero would mean that it is effectively thesame as not adding it back in. Other values may be used for themultiplicative weight.

Another way to describe the peak correction process is as follows.

Let z(r,t) represent the values of complex radar pulses at range r andtime t. Range samples r are separated in range by Δr represented by thebandwidth of the radar, and time samples t are separated in time by Δt,represented by the PRF of the radar.

For standard SAR imaging, the waveform that is used may be afully-filled temporal aperture. Therefore, over the time period of N*Δt,where N is the number of pulses that can be collected in this timeperiod with a given PRF, the URW representation is w(t)=1 for all t(i.e., a fully-filled temporal aperture), so the data used to generateimages would be z(r,t)*w(t)=z(r,t).

In cases where the URW is not unity for all t (i.e., the URW is notfully filled), a correction may be made for the effects of the URWsampling in preparation for image generation. The effect of the waveformsampling may iteratively be corrected as follows:

Let Z(r,f)=FFT(z(r,t)*w(t)) (e.g., Z(f) 1716), where FFT is the fastFourier transform of the sampled complex radar data for range rover atemporal subaperture period less than or equal to the full temporalaperture. The center time of the temporal subaperture is denoted by ts.

Iteratively, for data Z(r,f) at each range r, the following correctionis performed:

For iteration k, a maximum magnitude of Z(r,f,k) is identified, denotedas Z₀(k).

In a first part of step 1804, a threshold is selected to be a magnitudethat is less than or equal to Z₀(k), denoted by Z_(T)(k).

In a second part of step 1804, an array is formed Z′(r,f,k) such that:Z′(r,f,k)=Z(r,f,k) if |Z(r,f,k)|≧Z _(T)(k)Z′(r,f,k)=0 if |Z(r,f,k)|<Z _(T)(k)

In step 1806, a correction filter is created by convolving the frequencyresponse of the sampling filter by the array Z′(r,f,k) such thatZ″(r,f,k)=Z′(r,f,k)◯W(f) where W(f)=FFT(w(t)).

In step 1808, the data is then corrected using the following approach:Z(r,f,k+1)=Z(r,f,k)−Z″(r,f,k).

This iterative correction may be performed until a satisfactioncriterion or stopping condition is achieved. Useful stopping conditionsmay include, but are not limited to, the following: 1) when apre-defined number of iterations has been completed, 2) when the norm ofthe iterative correction is below a pre-defined threshold, 3) when theratio between the largest peak in the residual to the mean of theresidual noise level is below a pre-defined threshold, or 4) when theratio between the norm of the residual to the norm of the originalmeasurement is below a pre-defined threshold.

Utilizing the relationships between the sensor's attitude and statevector and the location of the area to be imaged, mapping relationshipsare constructed between the subaperture frame of reference (range r,frequency f, and time t_(S) at which the subaperture is collected) andthe ground plane (Cartesian positions x and y for the subaperture timet_(S)).

Temporal subapertures of n*Δt in length (sampled with the appropriateURW sampling w(t)) are used (referenced to a subaperture time t_(S))

-   -   z(r,t,t_(S))*w(t) sampled as defined by the URW sampling w(t).    -   For each range r, Z(r,f,t_(S)) is the URW corrected subaperture        data:    -   1. Z(x,y,t_(S))=map(Z(r,f,t_(S))) where map is a mapping between        (r,t) and (x,y) at subaperture time t_(S).    -   2. Compute the complex image Z(x,y)=sum(Z(x,y,t_(S)) where sum        is linear sum over subaperture time t_(S).

While Z(x,y) is the resulting complex valued image, |Z(x,y)^2| is usedfor the resultant detected image—for w(t)=1 for all t within eachsubaperture, this may be a standard SAR image.

The effect of applying the QR sampling pattern coupled with the peakcorrection algorithm on SAR imaging is shown in FIGS. 20A-B. As can beseen, a similar quality image has been produced using approximately halfof the radar pulses.

A critical benefit of these disclosed approaches may be the ability toprovide quality Doppler resolution (i.e., narrow main lobe width) whilesimultaneously being able to resolve these Doppler frequenciesunambiguously (i.e., individual sidelobes being as low as possible).Those of skill in the art will understand that radar data collected withthis waveform can be used to create many useful products other than SARimages. For example, moving target indication (MTI) and high resolutionterrain information (HRTI) may be two very useful radar products. Thewaveform and the correction algorithms described herein may allow thealgorithms of these other radar products to take advantage of the fineDoppler resolution and large unambiguous Doppler frequencies that thisinvention can provide. The use of this waveform and the correctionalgorithms in conjunction with other radar algorithms should not beinterpreted as causing a departure from the scope of the presentinvention.

In the embodiments described herein, the URW is defined and demonstratedin the time domain. However, the technology can be applied in spatialdomains, where radar antenna elements may comprise an array of antennaelements and use the identical approaches to achieve similar results.The antenna elements may be unequally spaced in a manner thatcorresponds to any of the unequal spatial separations discussed above.The antenna elements may instead be equally spaced, but may beselectively driven by a matrix of switches that are set to cause thedriven elements to be unequally spaced in a manner that corresponds toany of the unequal spatial separations discussed above.

Additionally, the technology described herein can also be applied inmultiple spatial and temporal domains, where pulse streams aretransmitted in time from driven radar antenna elements that comprise anarray of driven antenna elements in either one or two spatialdimensions, each being coded using the methods described herein. Theidentical approaches of coding and applying correction algorithms may beused to achieve similar results in multidimensional spatial and temporaldomains.

To illustrate these embodiments, the description of the URW coding maybe generalized as follows.

A single dimension may be represented by an aperture (A) and minimumincrements within the aperture (Δa). For the temporal domain, theaperture A may be a temporal aperture (T), which may be the period oftime during which the radar pulses are transmitted for a finite pulsetrain. Similarly, for the spatial domain, the aperture A may be aspatial aperture (D), which may be the full length over which the radarpulses are transmitted for a radar transmitter of finite length.

For the temporal domain, the increments within the aperture Δa may betime increments (Δt), representing the smallest time spacing betweenpulses. For the spatial domain, the increments within the aperture Δamay be distance increments (Δd), representing the smallest distancespacing between antenna elements.

With standard, evenly sampled SAR waveforms, image resolution may becomefiner as the temporal aperture (i.e., the period of time during whichthe radar pulses are transmitted) used for coherent integrationincreases. In one approach, an uneven sampling waveform, coupled withappropriately tailored post-processing algorithms, may be used toproduce images of similar quality and fewer radar pulses over the sametemporal aperture.

Similarly, with standard antennae having evenly spaced elements alongthe aperture, angular resolution may become finer as the spatialaperture (i.e., the full length over which the radar pulses aretransmitted) increases. In one approach, an uneven sampling waveform,coupled with appropriately tailored post-processing algorithms, may beused to produce radar returns of similar quality and fewer antennaelements over the same spatial aperture.

In one exemplary approach of the invention, such as in Paragraph [0064],the URW is defined in increments of Δt (i.e., the minimum timeseparation of the pulse train) such that the time separation betweenpulses is equal to integer multiples of Δt.

Similarly, in another exemplary approach, the URW can be defined inincrements of Δd (i.e., the minimum element separation of thetransmitter array) such that the distance separation between antennaelements is equal to integer multiples of Δd. For example, if theantenna array length is 1 meter, then a standard array over this spatialaperture of 1 meter may consist of 10 antenna elements, each separatedin distance by 0.1 meters. Thus, in this approach, the URW may bedefined by antenna elements that are separated by distances that aremultiples of 0.1 meters (0.2, 0.3, 0.4, 0.5, 0.6, 0.7, etc.). Forexample, a series of antenna elements that are arranged over the 1 meterspatial aperture may be described as follows: Antenna element 2 isseparated by 0.2 meters after antenna element 1, element 3 is separatedby 0.1 meters after element 2, element 4 is separated by 0.4 metersafter element 3, and element 5 is separated by 0.2 meters after element4.

As in Paragraph [0065], a convenient representation of the URW may beone where a binary string of ones and zeros represents where elementswithin the aperture A are active or inactive. For the time domain, thismay represent when pulses have or have not been transmitted at a giventime within the temporal aperture. For the spatial domain, this mayrepresent that a pulse is or is not transmitted from a given antennaelement within the spatial aperture.

Whether the aperture represents the time domain or the spatial domain,as in the examples above in Paragraph [0064]or Paragraph [00131], if aone (“1”) represents that an element is active at that integer multipleof Δa within the aperture A and a zero (“0”) represents that an elementis not active at that integer multiple of Δa within the aperture A, theURW example can be represented by a 10 character binary string[1,0,1,1,0,0,0,1,0,1]. Similarly, a standard waveform with a fullyfilled aperture can be represented as [1,1,1,1,1,1,1,1,1,1].

In radar applications such as imaging and moving target indication(MTI), the response function of the URW pattern may be very important.

In the temporal domain, the URW is defined as a function of time (e.g.,integer increments of Δt), so a Fourier representation (decomposition insine and cosine waves) shows how the URW is defined in frequency. In thespatial domain, the URW is defined as a function of distance (e.g.,integer increments of Δd), so a Fourier representation (decomposition insine and cosine waves) shows how the URW is defined in angle.

Different radar applications may be optimized by ensuring or designingcertain characteristics in the Fourier transform of the URW. With theinventive sampling and processing techniques disclosed herein, thesecharacteristics may be selected and utilized without sacrificingoperational efficiency or radar output qualities.

In radar applications, the narrowness of the width of the main lobe ofthe URW response may correspond to the radar resolution (whetherfrequency in the time domain or angle in the spatial domain).

A narrow main lobe may mean that the bulk of the energy response occursin a narrow range. This may indicate that the observed energy at aparticular frequency (or angle) generally occurs as the result of energythat is actually present at that frequency (or angle) and no others.Flat sidelobes may mean that frequencies (or angles) other than that ofthe main lobe have low energy responses. This may indicate that theobserved energy at a particular frequency (or angle) generally does notrespond to frequencies (or angles) other than the frequency (or angle)of interest.

In other words, having flat sidelobes may mean that the resultantsidelobe energy of the waveform response is distributed as evenly aspossible. This even distribution may ensure that any single sidelobepeak is as low as possible relative to the main lobe peak. Flatsidelobes may maximize the main lobe-to-maximum sidelobe energy ratio.In the temporal domain, this may result in elimination of temporalaliasing of the frequency response. In the spatial domain, this mayresult in elimination of grating lobes of the antenna response. Whetherconsidering the temporal domain or the spatial domain, these sidelobecharacteristics of the response function may be identical, even thoughthose skilled in the art may attribute them to different phenomena basedupon the domain upon which is being focused. Those skilled in the artwill recognize and appreciate that other radar applications may havedifferent desired optimal Fourier transform characteristics.

The primary characteristics of URW coding may be that (1) the spacingsbetween active elements (whether they are in the temporal domain, wherean active element represents that a pulse is transmitted at that integermultiple of Δt, or in the spatial domain, where an active elementrepresents that a pulse is transmitted at that antenna element) may beuneven, and that (2) the URW response function may have a narrow mainlobe and resultant sidelobe energy that is distributed as evenly aspossible. The URW examples above show that the spacing separations maybe substantially unequal. For example, the separation between at leasttwo neighboring active elements may be at least equal to twice theshortest separation between all of the other neighboring active elementsin the set. “Substantially unequal” is intended to distinguish betweenminor spatial and/or temporal variations due to loose factory toleranceswhich do not effectuate the goals/benefits which have been discussedherein from those variations which do.

One embodiment of this technology may be where radar pulses aretransmitted in a single dimension, where the aperture is defined in thetime domain, and the URW represents the time locations of active pulseswithin the pulse train, or over the temporal aperture.

Another embodiment of this technology may be where radar pulses aretransmitted in a single dimension, where the aperture is defined in thespatial domain, and the URW represents the locations of active antennaelements within the antenna array, or over the spatial aperture.

Further embodiments of the technology can be described by combining theURW coding descriptions in multiple dimensions.

In one exemplary embodiment, finite arrays of antennas can be arrangedin two dimensions (for example, one horizontal and one vertical). Whenthere is a two-dimensional antenna array, there may be two angles ofinterest for the angular response function, which may be generallydescribed as azimuth angle (for the horizontal) and elevation angle (forthe vertical). In this case, the two-dimensional URW response may be inazimuth angle and in elevation angle.

In another exemplary embodiment, URW coding can be applied in thetemporal domain and with a antenna array arranged in a single spatialdimension. In this case, the two-dimensional URW response may be infrequency and in angle, respectively.

In yet another exemplary embodiment, URW coding can be applied in thetemporal domain and with a antenna array arranged in two spatialdimensions. In this case, the three-dimensional URW response may be infrequency, in azimuth angle, and in elevation angle.

URW coding in multiple dimensions may achieve the same results as forone dimension, yielding beneficial main lobe and sidelobecharacteristics in the URW response functions and the appropriatepost-processing algorithms to achieve sidelobe energy reduction.

An illustrative embodiment for multidimensional URW coding utilizes thecombination of URW codes of single dimensions in the following way. LetURW₁ (i) be the ith element of the URW code in the first dimensionhaving n₁ elements, and let URW₂ (j) be the jth element of the URW codein the second dimension having n₂ elements. Then, the two dimensionalURW code may be represented by:URW(i,j)=0 for all j when i=1URW(i,j)=1 for all i≠1 when j=1URW(i,j)=(URW ₁(i)+URW ₂(j)+nstates−1)mod nstates,where nstates is equal to the total number of available states in theURW code, for all other (i,j).

In this example, there may be only two states, zero (“0”) and one (“1”),so nstates is equal to 2 and the modular arithmetic occurs in base 2.

As an example, let URW₁=[1,0,1,1,0] and let URW₂=[1,1,0,1,0]. Thecombined two-dimensional URW code may then be:

$\begin{matrix}1 & 0 & 1 & 1 & 0 \\1 & 0 & 1 & 1 & 0 \\1 & 1 & 0 & 0 & 1 \\1 & 0 & 1 & 1 & 0 \\0 & 0 & 0 & 0 & 0\end{matrix}\quad$

As another illustrative example, FIG. 21 shows the two dimensional URWcode where the one dimensional URW codes are quadratic residue (QR)codes of length 41 and 43, respectively. FIG. 22 shows the URW responsefunction for this two-dimensional URW code in logarithmic units. Notethe desired response characteristics of the narrow main lobe and flatsidelobes.

While the above URW coding examples illustrate the desired coding andresponse function characteristics, these illustrations may not precludethe use of other coding methods that achieve similar coding and responsefunction characteristics. Additionally, nothing in this descriptionprecludes the use of more than two states in the single dimension URWcodes or in the multidimensional combination of URW codes.

One such consideration for uneven sampling comes from the idea of randomor pseudo-random patterns. While these properties may not be achieved byall random patterns nor quite as well as the QR patterns, theflexibility of designing uneven sampling patterns of arbitrary lengthsand fractions may make such patterns useful. URW codes of singledimension can be generated using pseudorandom patterns, and combined asdescribed above.

Another embodiment can fill the multidimensional URW coding array withpseudorandom numbers without regard to the one dimensional URW codingcombination method described above.

Use of a multidimensional URW response can result in a URW response oflower dimensions. For example, let the multidimensional URW code beequal to:

$\begin{matrix}1 & 0 & 1 & 1 & 0 \\1 & 0 & 1 & 1 & 0 \\1 & 0 & 1 & 1 & 0 \\1 & 0 & 1 & 1 & 0 \\1 & 0 & 1 & 1 & 0\end{matrix}\quad$

This results in a two-dimensional URW coding array where all five rowsare equal to [1,0,1,1,0]. This embodiment could equivalently be modeledas a one-dimensional antenna array, coded with a single URW code of[1,0,1,1,0].

One embodiment of this technology may be in two dimensions, where thedimensions are time and one spatial dimension.

Another embodiment of this technology may be in two dimensions, wherethe dimensions are two spatial dimensions.

Another embodiment of this invention may be in three dimensions, wherethe dimensions are time and two spatial dimensions.

The URW correction algorithms described herein may operate identicallyin multiple dimensions as they have been demonstrated in a singledimension.

As an illustrative example, let z(ā) represent the values of complexradar pulses at various points in a dimension space ā, where ā may be inone or more dimensions. Samples a_(i) in each dimension are separatedwithin dimension i by Δa_(i). These increments within the aperture Δacould be time increments (Δt) in the temporal domain or distanceincrements (Δd) in the spatial domain.

The URW coding has the effect of sampling these complex radar values asz(ā)*w(ā), where w(ā) is the URW coding array in multiple dimensions,and the correction algorithm is applied as before, but in multipledimensions using the URW response function W(ã)=FFT(w(ā)).

FIG. 23 illustrates an exemplary radar system 2100 that may be used inthe implementation of the URW, including a transmitter 2102, a duplexer2110, a receiver 2120, a signal processor 2130, and a radar controller2140. The transmitter 2102 may be configured to generate a radio signalwith an oscillator such as a klystron or a magnetron 2104, while theduration and sequence of pulses, may be controlled by a modulator 2106.A waveguide (not shown) may link the transmitter 2102 and the antenna2190, while the duplexer 2110 may serve as a switch between the antenna2190 and the transmitter 2102 or the receiver 2120 for transmitting orreceiving signals when the antenna is used in both situations. Thereceived signals from the receiver 2120 may be processed by the signalprocessor 2130 before being further analyzed by the radar controller2140, which may control all the elements in radar system 2100 to performradar scans using the URW as described herein.

Those of skill in the art will understand that information and signalsmay be represented using any of a variety of different technologies andtechniques. For example, data, instructions, commands, information,signals, bits, symbols, and chips that may be referenced throughout theabove description may be represented by voltages, currents,electromagnetic waves, magnetic fields or particles, optical fields orparticles, or any combination thereof.

Those of skill will further appreciate that the various illustrativelogical blocks, modules, circuits, and algorithm steps described inconnection with the embodiments disclosed herein may be implemented aselectronic hardware, computer software, or combinations of both. Toclearly illustrate this interchangeability of hardware and software,various illustrative components, blocks, modules, circuits, and stepshave been described above generally in terms of their functionality.Whether such functionality is implemented as hardware or softwaredepends upon the particular application and design constraints imposedon the overall system. Skilled artisans may implement the describedfunctionality in varying ways for each particular application, but suchimplementation decisions should not be interpreted as causing adeparture from the scope of the present invention.

The various illustrative logical blocks, modules, and circuits describedin connection with the embodiments disclosed herein may be implementedor performed with a general purpose processor, a digital signalprocessor (DSP), an application specific integrated circuit (ASIC), afield programmable gate array (FPGA) or other programmable logic device,discrete gate or transistor logic, discrete hardware components, or anycombination thereof designed to perform the functions described herein.A general purpose processor may be a microprocessor, but in thealternative, the processor may be any conventional processor,controller, microcontroller, or state machine. A processor may also beimplemented as a combination of computing devices, e.g., a combinationof a DSP and a microprocessor, a plurality of microprocessors, one ormore microprocessors in conjunction with a DSP core, or any other suchconfiguration. A processing system may include a processor and memory,as well as a combination of other components.

The steps of a method or algorithm described in connection with theembodiments disclosed herein may be embodied directly in hardware, in asoftware module executed by a processor, or in a combination of the two.A software module may reside in RAM memory, flash memory, ROM memory,EPROM memory, EEPROM memory, registers, hard disk, a removable disk, aCD-ROM, or any other form of storage medium known in the art. Anexemplary storage medium may be coupled to the processor such theprocessor can read information from, and write information to, thestorage medium. In the alternative, the storage medium may be integralto the processor. The processor and the storage medium may reside in anASIC. The hardware, including the ASIC, may reside in a radar platform.In the alternative, the processor and the storage medium may reside asdiscrete components in the radar platform.

The components, steps, features, objects, benefits and advantages whichhave been discussed are merely illustrative. None of them, nor thediscussions relating to them, are intended to limit the scope ofprotection in any way. Numerous other embodiments are also contemplated.These include embodiments which have fewer, additional, and/or differentcomponents, steps, features, objects, benefits and advantages. Thesealso include embodiments in which the components and/or steps arearranged and/or ordered differently.

Unless otherwise stated, all measurements, values, ratings, positions,magnitudes, sizes, and other specifications which are set forth in thisspecification, including in the claims which follow, are approximate,not exact. They are intended to have a reasonable range which isconsistent with the functions to which they relate and with what iscustomary in the art to which they pertain.

All articles, patents, patent applications, and other publications whichhave been cited in this disclosure are hereby incorporated herein byreference.

The phrase “means for” when used in a claim is intended to and should beinterpreted to embrace the corresponding structures and materials whichhave been described and their equivalents. Similarly, the phrase “stepfor” when used in a claim is intended to and should be interpreted toembrace the corresponding acts which have been described and theirequivalents. The absence of these phrases in a claim mean that the claimis not intended to and should not be interpreted to be limited to any ofthe corresponding structures, materials, or acts or to theirequivalents.

Nothing which has been stated or illustrated is intended or should beinterpreted to cause a dedication of any component, step, feature,object, benefit, advantage, or equivalent to the public, regardless ofwhether it is recited in the claims.

The scope of protection is limited solely by the claims which nowfollow. That scope is intended and should be interpreted to be as broadas is consistent with the ordinary meaning of the language which is usedin the claims when interpreted in light of this specification and theprosecution history which follows and to encompass all structural andfunctional equivalents.

1. A radar transmission system comprising: a transmitter systemconfigured to generate one or more radar signals; and an antenna systemhaving spatially-separated elements and configured to radiate the one ormore radar signals from the spatially-separated elements, wherein thetransmitter system and/or the antenna system are configured such thatthe radiated radar signals include a pattern of spatially-separatedradar pulses, each from a different one of the spatially-separatedantenna elements, the pattern of pulses having: at least two neighboringradar pulses that have a spatial separation that is substantiallyunequal to the spatial separation between at least two other neighboringradar pulses in the pattern of pulses; a mainlobe radiation pattern witha width that is near or substantially equal to the minimum possiblemainlobe width; and sidelobe radiation patterns with substantially evenenergy distribution.
 2. The radar transmission system of claim 1 furthercomprising a processing system configured to generate pulses using aFourier transform which are used by the transmitter system to generatethe one or more radar signals.
 3. The radar transmission system of claim1 wherein the radiated pattern of pulses has a quadratic residue (QR)pattern.
 4. The radar transmission system of claim 1 wherein theradiated pattern of pulses has a pseudo-random pattern.
 5. The radartransmission system of claim 1 wherein: the elements of the antennasystem are spatially-separated in two dimensions; the pattern of radarpulses includes pulses spatially-separated in the two dimensions, andthe substantially unequal separation includes substantially unequalseparation in the spatial locations from which the radar pulses areradiated by the antenna system in both of the two dimensions.
 6. Theradar transmission system of claim 1 wherein the transmitter system isconfigured such that the radiated radar signals include a pattern oftime-separated radar pulses having at least two sequential radar pulseswith a time separation that is substantially unequal to the timeseparation between at least two other sequential radar pulses in thepattern of pulses.
 7. The radar transmission system of claim 1 whereinthe antenna elements are unequally spaced.
 8. The radar transmissionsystem of claim 1 wherein the antenna elements are equally spaced, butthe transmission system is configured to selectively drive the elementsso as to cause the driven elements to have the substantially unequalspatial separations.
 9. Non-transitory, tangible, computer-readablestorage media containing programming code which, when executed by acomputer system, causes an antenna system to radiate radar signals whichinclude a pattern of pulses having: at least two neighboring radarpulses that have a spatial separation that is substantially unequal tothe spatial separation between at least two other neighboring radarpulses in the pattern of pulses; and a mainlobe radiation pattern with awidth that is near or substantially equal to the minimum possiblemainlobe width; and sidelobe radiation patterns with substantially evenenergy distribution.
 10. The computer-readable storage media of claim 9wherein the programming code, when executed by a computer system, causesthe computer system to generate pulses using a Fourier transform whichare converted into the radar signals by a transmitter system.
 11. Thecomputer-readable storage media of claim 9 wherein the pattern of radarpulses has a quadratic residue (QR) pattern.
 12. The computer-readablestorage media of claim 9 wherein the pattern of radar pulses has apseudo-random pattern.
 13. The computer-readable storage media of claim9 wherein the pattern of radar pulses includes pulsesspatially-separated in two dimensions; and the substantially unequalseparation includes substantially unequal separation in both of the twodimensions.
 14. The computer-readable storage media of claim 9 whereinthe programming code, when executed by the computer system, causes theradiated radar signals to include a pattern of time-separated radarpulses having at least two sequential radar pulses with a timeseparation that is substantially unequal to the time separation betweenat least two other sequential radar pulses in the pattern of pulses. 15.A radar reception system comprising: a receiver configured to receive aradar signal which includes a first data set having a plurality ofvalues based on a radar waveform return from a set of transmitted radarpulses; and a processing system configured to create a second data setcomprising the first data set minus at least one significant value fromthe first data set and its effects on other values within the first dataset when the set of transmitted radar pulses was transmitted with: aspatial separation between at least two neighboring pulses that issubstantially unequal to the spatial separation between at least twoother neighboring pulses in the set; a mainlobe radiation pattern with awidth that is near or substantially equal to the minimum possible width;and sidelobe radiation patterns with a substantially even distributionof energy.
 16. The radar reception system of claim 15 wherein theprocessing system is configured to: create a third data set comprisingthe at least one significant value from the first data set; and combinethe second and third datasets.
 17. The radar reception system of claim15 wherein the first data set includes a plurality of transformedvalues.
 18. The radar reception system of claim 17 wherein the pluralityof transformed values are frequency values.
 19. The radar receptionsystem of claim 15 wherein the at least one significant value includes apeak value in a frequency domain.
 20. The radar reception system ofclaim 15 wherein the second data set includes a number of peak valuesfrom the first data set chosen based on predetermined selectioncriteria.
 21. The radar reception system of claim 15 wherein theprocessing system is configured to determine the effects of the at leastone significant value by calculating a plurality of propagated effectsfrom the at least one significant value.
 22. The radar reception systemof claim 15 wherein the processing system is configured to create thesecond data set by: identifying at least one peak value in the firstdata set; creating a peak correction function approximation using the atleast one peak value; and removing the peak correction functionapproximation from the first data.
 23. The radar reception system ofclaim 15 wherein: the pattern of radar pulses includes pulsesspatially-separated in two dimensions; and the substantially unequalseparation includes substantially unequal separation in both of the twodimensions.
 24. The radar reception system of claim 15 wherein theradiated radar signals include a pattern of time-separated radar pulseshaving at least two sequential radar pulses with a time separation thatis substantially unequal to the time separation between at least twoother sequential radar pulses in the pattern of pulses. 25.Non-transitory, tangible, computer-readable storage media containingprogramming code which, when executed by a computer system, creates asecond data set comprising a first data set having a plurality of valuesbased on a radar waveform return from a set of transmitted radar pulsesminus at least one significant value from the first data set and itseffects on other values within the first data set when the set oftransmitted radar pulses has: a spatial separation between at least twoneighboring pulses that is substantially unequal to the spatialseparation between at least two other neighboring pulses in the set; amainlobe radiation pattern with a width that is near or substantiallyequal to the minimum possible width; and sidelobe radiation patternswith a substantially even distribution of energy.
 26. Thecomputer-readable storage media of claim 25 wherein the programmingcode, when executed by the computer system: creates a third data setcomprising the at least one significant value from the first data set;and combines the second and third datasets.
 27. The computer-readablestorage media of claim 25 wherein the first data set includes aplurality of transformed values.
 28. The computer-readable storage mediaof claim 27 wherein the plurality of transformed values are frequencyvalues.
 29. The computer-readable storage media of claim 25 wherein theat least one significant value includes a peak value in a frequencydomain.
 30. The computer-readable storage media of claim 25 wherein thesecond data set includes a number of peak values from the first data setchosen based on predetermined selection criteria.
 31. Thecomputer-readable storage media of claim 25 wherein the programmingcode, when executed by the computer system, determines the effects ofthe at least one significant value by calculating a plurality ofpropagated effects from the at least one significant value.
 32. Thecomputer-readable storage media of claim 25 wherein the programmingcode, when executed by the computer system, creates the second data setby: identifying at least one peak value in the first data set; creatinga peak correction function approximation using the at least one peakvalue; and removing the peak correction function approximation from thefirst data.
 33. The computer-readable storage media of claim 25 wherein:the set of radar pulses are spatially-separated in two dimensions; andthe substantially unequal separation includes substantially unequalseparation in both of the two dimensions.
 34. The computer-readablestorage media of claim 25 wherein the set of radar pulses include apattern of time-separated radar pulses having at least two sequentialradar pulses with a time separation that is substantially unequal to thetime separation between at least two other sequential radar pulses inthe pattern of pulses.
 35. A radar transmission system comprising: atransmitter system configured to generate one or more radar signals; andan antenna system having spatially-separated elements and configured toradiate the one or more radar signals from the spatially-separatedelements, wherein the transmitter system and/or the antenna system areconfigured such that the radiated radar signals include a pattern ofspatially-separated radar pulses, each from a different one of thespatially-separated antenna elements, the pattern of radar pulses havingat least two neighboring radar pulses that have a spatial separationthat is at least twice the shortest spatial separation between at leasttwo other neighboring radar pulses in the pattern of pulses.
 36. Theradar transmission system of claim 35 further comprising a processingsystem configured to generate pulses using a Fourier transform which areused by the transmitter system to generate the one or more radarsignals.
 37. The radar transmission system of claim 35 wherein theradiated pattern of pulses has a quadratic residue (QR) pattern.
 38. Theradar transmission system of claim 35 wherein the radiated pattern ofpulses has a pseudo-random pattern.
 39. The radar transmission system ofclaim 35 wherein: the elements of the antenna system arespatially-separated in two dimensions; the pattern of radar pulsesincludes pulses spatially-separated in the two dimensions, and thesubstantially unequal separation includes substantially unequalseparation in the spatial locations from which the radar pulses areradiated by the antenna system in both of the two dimensions.
 40. Theradar transmission system of claim 35 wherein the transmitter system isconfigured such that the radiated radar signals include a pattern oftime-separated radar pulses having at least two sequential radar pulseswith a time separation that is substantially unequal to the timeseparation between at least two other sequential radar pulses in thepattern of pulses.
 41. The radar transmission system of claim 35 whereinthe antenna elements are unequally spaced.
 42. The radar transmissionsystem of claim 35 wherein the antenna elements are equally spaced, butthe transmission system is configured to selectively drive the elementsso as to cause the driven elements to have the substantially unequalspatial separations.
 43. Non-transitory, tangible, computer-readablestorage media containing programming code which, when executed by acomputer system, causes an antenna system to radiate radar signals whichinclude a pattern of pulses having at least two neighboring radar pulsesthat have a spatial separation that is at least twice the shortestspatial separation between at least two other neighboring radar pulsesin the pattern of pulses.
 44. The computer-readable storage media ofclaim 43 wherein the programming code, when executed by a computersystem, causes the computer system to generate pulses using a Fouriertransform which are converted into the radar signals by a transmittersystem.
 45. The computer-readable storage media of claim 43 wherein thepattern of radar pulses has a quadratic residue (QR) pattern.
 46. Thecomputer-readable storage media of claim 43 wherein the pattern of radarpulses has a pseudo-random pattern.
 47. The computer-readable storagemedia of claim 43 wherein the pattern of radar pulses includes pulsesspatially-separated in two dimensions; and the substantially unequalseparation includes substantially unequal separation in both of the twodimensions.
 48. The computer-readable storage media of claim 43 whereinthe programming code, when executed by the computer system, causes theradiated radar signals to include a pattern of time-separated radarpulses having at least two sequential radar pulses with a timeseparation that is substantially unequal to the time separation betweenat least two other sequential radar pulses in the pattern of pulses. 49.A radar reception system comprising: a receiver configured to receive aradar signal which includes a first data set having a plurality ofvalues based on a radar waveform return from a set of transmitted radarpulses; and a processing system configured to create a second data setcomprising the first data set minus at least one significant value fromthe first data set and its effects on other values within the first dataset when the set of transmitted radar pulses was transmitted with apattern of radar pulses having at least two neighboring radar pulsesthat have a spatial separation that is at least twice the shortestspatial separation between at least two other neighboring radar pulsesin the pattern of pulses.
 50. The radar reception system of claim 49wherein the processing system is configured to: create a third data setcomprising the at least one significant value from the first data set;and combine the second and third datasets.
 51. The radar receptionsystem of claim 49 wherein the first data set includes a plurality oftransformed values.
 52. The radar reception system of claim 51 whereinthe plurality of transformed values are frequency values.
 53. The radarreception system of claim 49 wherein the at least one significant valueincludes a peak value in a frequency domain.
 54. The radar receptionsystem of claim 49 wherein the second data set includes a number of peakvalues from the first data set chosen based on predetermined selectioncriteria.
 55. The radar reception system of claim 49 wherein theprocessing system is configured to determine the effects of the at leastone significant value by calculating a plurality of propagated effectsfrom the at least one significant value.
 56. The radar reception systemof claim 49 wherein the processing system is configured to create thesecond data set by: identifying at least one peak value in the firstdata set; creating a peak correction function approximation using the atleast one peak value; and removing the peak correction functionapproximation from the first data.
 57. The radar reception system ofclaim 49 wherein: the pattern of radar pulses includes pulsesspatially-separated in two dimensions; and the substantially unequalseparation includes substantially unequal separation in both of the twodimensions.
 58. The radar reception system of claim 49 wherein theradiated radar signals include a pattern of time-separated radar pulseshaving at least two sequential radar pulses with a time separation thatis substantially unequal to the time separation between at least twoother sequential radar pulses in the pattern of pulses. 59.Non-transitory, tangible, computer-readable storage media containingprogramming code which, when executed by a computer system, creates asecond data set comprising a first data set having a plurality of valuesbased on a radar waveform return from a set of transmitted radar pulsesminus at least one significant value from the first data set and itseffects on other values within the first data set when the set oftransmitted radar pulses has at least two neighboring radar pulses thathave a spatial separation that is at least twice the shortest spatialseparation between at least two other neighboring radar pulses in thepattern of pulses.
 60. The computer-readable storage media of claim 59wherein the programming code, when executed by the computer system:creates a third data set comprising the at least one significant valuefrom the first data set; and combines the second and third datasets. 61.The computer-readable storage media of claim 59 wherein the first dataset includes a plurality of transformed values.
 62. Thecomputer-readable storage media of claim 61 wherein the plurality oftransformed values are frequency values.
 63. The computer-readablestorage media of claim 59 wherein the at least one significant valueincludes a peak value in a frequency domain.
 64. The computer-readablestorage media of claim 59 wherein the second data set includes a numberof peak values from the first data set chosen based on predeterminedselection criteria.
 65. The computer-readable storage media of claim 59wherein the programming code, when executed by the computer system,determines the effects of the at least one significant value bycalculating a plurality of propagated effects from the at least onesignificant value.
 66. The computer-readable storage media of claim 59wherein the programming code, when executed by the computer system,creates the second data set by: identifying at least one peak value inthe first data set; creating a peak correction function approximationusing the at least one peak value; and removing the peak correctionfunction approximation from the first data.
 67. The computer-readablestorage media of claim 59 wherein: the set of radar pulses arespatially-separated in two dimensions; and the substantially unequalseparation includes substantially unequal separation in both of the twodimensions.
 68. The computer-readable storage media of claim 59 whereinthe set of radar pulses include a pattern of time-separated radar pulseshaving at least two sequential radar pulses with a time separation thatis substantially unequal to the time separation between at least twoother sequential radar pulses in the pattern of pulses.